The coordinate plane: quadrants and distances along grid lines

Warm-up

Three quick questions from earlier lessons.

Discover

The point $(3, -2)$ : where is it?

3 right, 2 down
2 right, 3 down

Key idea

Four quadrants; distances along a grid line.

A point

(x, y)

x

right (left if negative) and

y

up (down if negative). The axes split the plane into quadrants I–IV counterclockwise from upper right. Two points with the same $x$ (or same

y

) are

|y_1 - y_2|

apart; across an axis, add the absolute values.

Worked example

$(-3, 4)$ and $(5, 4)$ .

Horizontal distance

Same y.

3 + 5 = 8

3 to 0, then 5.

Your turn, guided

Your turn: distance between $(2, -6)$ and $(2, 1)$ .

7

6 + 1.

Practice ★

In which quadrant is the point $(-9, 5)$ ?
1. Quadrant II (left, up)
2. Quadrant I (right, up)
3. Quadrant IV (right, down)
In which quadrant is the point $(-6, 2)$ ?
1. Quadrant II (left, up)
2. Quadrant I (right, up)
3. Quadrant IV (right, down)

What is the distance between $(9, 1)$ and $(9, -5)$ ?

Watch out!

Practice ★★

What is the distance between $(-2, 1)$ and $(9, 1)$ ?
What is the distance between $(-6, -4)$ and $(2, -4)$ ?

Boss problem. A rectangle has vertices $(-2, 2)$ , $(3, 2)$ , $(3, -3)$ and $(-2, -3)$ .

Exit ticket

Three questions to check you have got it.

What is the distance between $(9, 1)$ and $(9, -5)$ ?
What is the distance between $(9, 5)$ and $(9, -6)$ ?
What is the distance between $(7, 2)$ and $(7, -3)$ ?

Summary card

The coordinate plane

x right/left, y up/down; same coordinate: subtract or add across 0.

Watch out: x comes first.

End of the lesson

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